Finding RootsMETHOD: To find the roots of a polynomial, first try to factor it. This which works in many examples in calculus courses. For quadratic polynomials, or quadratic factors in polynomials, use the quadratic formula.There is no general method for finding the root of an arbitrary polynomial. The best thing to do is to find a numerical approximation of the root using a calculator or computer. Example 1. Find the roots of
Solution: Try factoring. 2 = 1^{.}2 or
(1)(2). The only possibilities are
Example 2. Find the roots of
Solution: Try factoring. 2 = 1^{.}2 or
(1)(2). The only possibilities are
Example 3. Find the roots of Solution: Factoring doesn't work (trust us!), so use the quadratic formula: The roots are
Example 4. Find the roots of Solution: Try factoring out a linear term, or use trial and error. Say you find the factor of (x + 2). Then write x^{3}  2 x^{2}  x  2 = (x +2)(x^{2}  1). The roots, then, are x = 2, x = 1, and x = 1.
